Existence of Incomplete Transversal Designs with Block Size Five and Any Index λ

被引：19
作者：
Abel R.J.R. [1 ]
Colbourn C.J. [2 ]
Yin J. [3 ]
Zhang H. [4 ]
机构：
[1] School of Mathematics, University of New South Wales, Kensington
[2] Combinatorics and Optimization, University of Waterloo, Waterloo
[3] Department of Mathematics, Suzhou University
[4] Computer Science, University of Iowa, Iowa City
来源：
Designs, Codes and Cryptography | 1997年 / 10卷 / 3期
基金：
加拿大自然科学与工程研究理事会; 美国国家科学基金会;
关键词：
Group divisible design; Latin square; Orthgonal array; Pairwise balanced design; Transversal design;
D O I：
10.1023/A:1008232418845
中图分类号：
学科分类号：
摘要：
The basic necessary condition for the existence of a T D (5, λ; υ) - T D (5, λ; u), namely υ ≥ 4u, is shown to be sufficient for any λ ≥ 1, except when (υ, u) = (6, 1) and λ = 1, and possibly when (υ, u) = (10, 1) or (52, 6) and λ = 1. For the case λ = 1, 86 new incomplete transversal designs are constructed. Several construction techniques are developed, and some new incomplete TDs with block size six and seven are also presented.
引用
收藏
页码：275 / 307
页数：32
相关论文
共 37 条
  • [31] Roth R., Peters M., Four pairwise orthogonal latin squares of order 24, J. Combin. Theory (A), 44, pp. 152-155
  • [32] Wallis W.D., Zhu L., Orthogonal latin squares with small subsquares: Combinatorial Mathematics, 10(Adelaide, 1982), Lecture Notes in Math., 1036, pp. 398-409, (1983)
  • [33] Wilson R.M., Concerning the number of mutually orthogonal latin squares, Discrete Math., 9, pp. 181-198, (1974)
  • [34] Wilson R.M., A few more squares: Proc. 5th S-E Conf, On Combinatorics, Graph Theory and Computing, pp. 675-680, (1974)
  • [35] Wilson R.M., Constructions and use of pairwise balanced designs, Math. Centre Tracts, 55, pp. 18-41, (1974)
  • [36] Yin J., On the packing of pairs by quintuples with index 2, Ars Combin., 31, pp. 287-301, (1991)
  • [37] Zhu L., Some results on orthogonal latin squares with orthogonal subsquares, Utilitas Math., 25, pp. 241-248, (1984)
1234